The input impedance of the AXE FX II is 1MOhm (switchable to lower values!) what is usually even enough for passive piezo pickups if the cable is short, let's say up to 2m. Anyway most acoustic guitars have an internal buffer preamp so that a cable length up to 10m shouldn't be a problem to.
I often change between (passive) electric guitars and acoustic guitars with internal preamp and I plug both into a digital wireless transmitter with 1MOhm input impedance as well. For the cable to the transmitter is around 0,6m there is even no problem with my acoustic guitars with passive (Schatten) pickup.
When it comes to the preset I go like this:
INPUT: Impedance set to 1MOhm, noisegate with low value to get rid of the guitar's preamp hiss.
Compressor: Only slightly, like you would in a studio recording of an acoustic guitar, same with Reverb
Delay: For some songs it might be apparent FX ("Eagles-sound", tape delay on bluesy songs), for background strumming it does also work good to use a stereo delay with minimum feedback, one side very short delay (f.e.1ms) and the other side 15ms or more. Then you'll sound nearly like two guitars panned L and R and the center remains free for the vocals...
Chorus: Also allowed for acoustic guitars, but only a very small amount imo
Now it becomes tricky:
You could do a tone matching with a good studio recording of an acoustic guitar and use this to enhance the "direct piezo sound" with that. Blend it in to your taste, this makes even the piezo sound of an electric guitar sound great!